Abstract
In this paper, we investigate the diversity, capacity and complexity issues of cooperative Zero-Padding (ZP)-Orthogonal Frequency Division Multiplexing (OFDM) communication. We consider cooperative ZP-OFDM communication over a multipath Rayleigh channel and with multiple Carrier Frequency Offsets (CFOs) existing at different relays. We use a cooperative tall Toeplitz scheme to achieve full cooperative and multipath diversity, while simultaneously combat the CFOs. Importantly, this full diversity scheme only requires Linear Equalizers (LEs), such as Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) equalizers, an issue which reduces the system complexity when compared to a Maximum-Likelihood Equalizer (MLE) or other near-MLEs. Theoretical analysis of the proposed cooperative tall Toeplitz scheme is provided on the basis of the analytical upper bound of the channel orthogonality deficiency derived in this paper. Utilizing only low-complexity linear equalizers, theoretical analysis and simulation results show that the proposed Toeplitz scheme achieves the full cooperative, multipath and outage diversity.
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Abbreviations
- AF:
-
Amplify-and-Forward
- AWGN:
-
Additive White Gaussian Noise
- BER:
-
Bit Error Rate
- CDFs:
-
Cumulative Density Functions
- CF:
-
Compress-and-Forward
- CFOs:
-
Carrier Frequency Offsets
- CP:
-
Cyclic Prefix
- CR:
-
Cognitive Radio
- DF:
-
Decode-and-Forward
- DPS:
-
Digital Phase Sweeping
- ECMA:
-
European Computer Manufacturers Association
- FFT:
-
Fast Fourier Transform
- IFFT:
-
Inverse Fast Fourier Transform
- ISI:
-
Inter-Symbol-Interference
- LEs:
-
Linear Equalizers
- MB:
-
Multi-Band
- MLE:
-
Maximum-Likelihood Equalizer
- MMSE:
-
Minimum Mean Square Error
- od :
-
orthogonality deficiency
- OFDM:
-
Orthogonal Frequency Division Multiplexing
- OLA:
-
Overlap and Add
- PSD:
-
Power Spectral Density
- SD:
-
Sphere Decoding
- SNR:
-
Signal-to-Noise Ratio
- STC:
-
Space Time Coding
- STFC:
-
Space-Time-Frequency Coding
- SFC:
-
Space Frequency Coding
- UWB:
-
Ultra Wide Band
- ZF:
-
Zero-Forcing
- ZP:
-
Zero-Padding
- (·)T :
-
Transpose of (·)
- (·)* :
-
Conjugate of (·)
- (·)H :
-
Hermitian of (·)
- (·)−1 :
-
Inverse of (·)
- \({\left(\cdot \right)^{\dagger}}\) :
-
Pseudo inverse of (·)
- \({\forall}\) :
-
For all
- \({\left| \cdot \right|}\) :
-
Absolute value of a scalar or cardinality of a set
- \({\left\| \cdot \right\|\quad}\) :
-
2-Norm of a vector/matrix
- argue min (·):
-
Argument of minimum of (·)
- diag (·):
-
Diagonal matrix with main diagonal (·)
- det (·):
-
Determinant of (·)
- lim (·):
-
Limit of (·)
- log (·):
-
Logarithm with base 10
- log 2 (·):
-
Logarithm with base 2
- max (·):
-
Maximum of (·)
- od (·):
-
Orthogonality deficiency of matrix (·)
- O (·):
-
Landau notation
- Prob (·):
-
Probability of (·)
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Lu, H., Xu, T., Nikookar, H. et al. Performance Analysis of the Cooperative ZP-OFDM: Diversity, Capacity and Complexity. Wireless Pers Commun 68, 587–608 (2013). https://doi.org/10.1007/s11277-011-0470-9
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DOI: https://doi.org/10.1007/s11277-011-0470-9